Quantum phase transitions and critical behaviors in the two-mode three-level quantum Rabi model

TL;DR

This paper investigates quantum phase transitions in an extended two-mode, three-level quantum Rabi model, revealing a rich phase diagram with normal and superradiant phases, characterized by second-order and discontinuous transitions, and identifies the model's universality class.

Contribution

The study provides an analytical solution for the model's phase diagram, including critical exponents and scaling functions, and characterizes the nature of phase transitions and symmetry breaking.

Findings

Identified three distinct phases: normal and two superradiant.

Characterized second-order and discontinuous quantum phase transitions.

Derived critical exponents and verified universality class.

Abstract

We explore an extended quantum Rabi model describing the interaction between a two-mode bosonic field and a three-level atom. Quantum phase transitions of this few degree of freedom model is found when the ratio $\eta$ of the atom energy scale to the bosonic field frequency approaches infinity. An analytical solution is provided when the two lowest-energy levels are degenerate. According to it, we recognize that the phase diagram of the model consists of three regions: one normal phase and two superradiant phases. The quantum phase transitions between the normal phase and the two superradiant phases are of second order relating to the spontaneous breaking of the discrete $Z_{2}$ symmetry. On the other hand, the quantum phase transition between the two different superradiant phases is discontinuous with a phase boundary line relating to the continuous $U(1)$ symmetry. For a large enough but finite $\eta$, the scaling function and critical exponents are derived analytically and verified numerically, from which the universality class of the model is identified.